What the colour distance test shows
RGB distance is nearly useless perceptually. Two greens a long way apart numerically can look identical, while two blues that are numerically close look obviously different, because RGB space is not uniform with respect to human vision.
CIE Lab was built to fix that: equal distances in Lab correspond roughly to equal perceived differences. A Delta E of about 2.3 is the just-noticeable difference, which is the threshold that makes the number mean something concrete.
What a Delta E number means
Below 1, the two colours are indistinguishable. Below 2.3 they are at the threshold — you might catch it side by side and never apart. Between 2.3 and 5 they are noticeably different when adjacent. Above 10 they are simply different colours.
This matters when you are checking whether two greys in a design system are actually doing different jobs, or whether a brand colour has drifted between two files.